Projectiles

ARTICLE IN PRESS

International Journal of Impact Engineering ] (]]]]) ]]]–]]] www.elsevier.com/locate/ijimpeng

Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered plates N.K. Gupta, M.A. Iqbal, G.S. Sekhon Department of Applied Mechanics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India Received 6 February 2006; received in revised form 31 July 2006; accepted 10 November 2006

Abstract The present study is based on the experimental and numerical investigations of deformation behavior of layered aluminum plates of different thicknesses under the impact of flat, ogive and hemispherical nosed steel projectiles. Thin-layered plates arranged in various combinations were normally impacted at different velocities with the help of a pneumatic gun. Ballistic limit velocity and the residual velocity of the projectiles for each layered combination were obtained experimentally as well as from the finite element code, and these were compared with those of the single plates of equivalent thicknesses. For two layers, the residual velocity was comparable to that of the single plate, however, when the number of layers was increased the velocity drop was found to be higher in the case of the single plate. Ogive nosed projectile was found to be the most efficient penetrator of the layered target. Hemispherical nosed projectile required maximum energy for perforation. Deformation profiles of the target plates in the layered combinations were measured, and it was found that hemispherical nosed projectile caused highest plastic deformation of target plates. Numerical simulation of the problem was carried out using finite element code ABAQUS. Explicit solution technique of the code was used to analyze the perforation phenomenon. Results of the finite element analysis were compared with experiments and a good agreement between the two was found. r 2006 Published by Elsevier Ltd. Keywords: Deformation mechanism; Nose shape; Abaqus; Layered plate

1. Introduction When a single plate subjected to impact by projectiles is replaced by several layered thin plates to give equivalent thickness, the mode of deformation may change from shearing to bending and membrane stretching of individual plates. This phenomenon may cause higher penetration resistance to the projectiles impacted on layered plates. Marom and Bonder [1] carried out analytical and experimental studies on the ballistic resistance of thin, flat beams of pure aluminum and 6061-T6 aluminum alloy, arranged in various layers in contact as well as spaced, and impacted by 0.22 in caliber projectiles. The multi-layered beams in contact showed greater resistance to penetration than the equivalent monolithic beams. Corran et al. [2] investigated the performance of multilayered steel plates under projectile impact, they found that Corresponding author. Tel.: +91 11 2659 1178; fax: +91 11 658 1119.

E-mail address: [email protected] (N.K. Gupta).

the layers placed in contact were superior to equivalent monolithic plates when the response of individual plates changed from petalling and shearing to membrane stretching. An investigation of the ballistic resistance of monolithic and adjacent layered targets of 2024-0 aluminum and polycarbonate was conducted by Radin and Goldsmith [3] with flat and 601 conically nosed projectiles of 12.57 mm diameter, striking at 50–210 m/s impact velocities. Analytical models were used to calculate the residual velocity in terms of initial projectile velocity, ballistic limit, mass of the projectile and plug. The predicted ballistic limit was found to be in fair agreement for the case of flat nosed projectiles and in good agreement in the case of pointed nosed projectiles. Layered targets were found to be less effective than the equivalent monolithic targets. Nurick and Walter [4] studied the penetration resistance of layered steel plates using conical and flat nosed projectiles. The ballistic limit of monolithic plates was 4–8% higher than of the in-contact layered targets of equivalent thickness.

0734-743X/$ - see front matter r 2006 Published by Elsevier Ltd. doi:10.1016/j.ijimpeng.2006.11.004 Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS 2

N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

Gupta and Madhu [5,6] studied the normal and oblique impact of armor-piercing projectiles of 6.2 mm diameter on single and layered plates of mild steel, RHA steel and aluminum of thickness varying from 6 to 40 mm. Determination of a plate thickness (t*), for which the incident velocity is the ballistic limit, was carried out. Simple models were developed to determine the residual velocity for a plate of thickness lesser than t*, and to relate t* with the hardness of the material. It was found that for relatively thicker plates in two layers, the residual velocity was comparable to single plate of equal thickness. However, for thin plates in-contact layered combination gave higher residual velocity for all the materials tested. Johnson and Cook [7] presented the Lagrangian EPIC code computations for oblique, yawed-rod impact on thin single as well as spaced steel plates at various velocities. The results were found in good agreement with experiments as well as previously published computational results with Eularian MESA code. The computation time required in the case of EPIC code was found comparatively lesser than that of the MESA code. Borvik et al. [8,9] studied the behavior of 12 mm thick single steel plates impacted by blunt, conical and hemispherical nosed projectiles of 20 mm diameter. Blunt nosed projectiles were more efficient penetrators than hemispherical and conical projectiles at low velocities. At higher impact velocities however, conical nosed projectiles required least energy to perforate the target plates. Good agreement between experimental and corresponding finite element results was found. It was shown that adaptive meshing is desirable in 2D impact simulations with conical and hemispherical nosed projectiles. Numerical simulations carried out with adaptive meshing also showed good agreement with the experimental results. The present study deals with the experimental and numerical investigations of projectile impact on layered aluminum target plates of 255 mm diameter. Thin-layered plates of 0.5, 0.71, 1 and 1.5 mm thicknesses were normally impacted by flat, ogive and hemispherical nosed projectiles of 19 mm diameter and 52.5 g mass. The projectiles were made of EN-24 steel. It was observed that as the impact velocity increases the velocity drop of the projectiles decreases. Impact and residual velocity curves of layered plates are compared with those of the single plates of equivalent thickness. Deformation profiles of the layered target plates were measured, and these showed that the hemispherical nosed projectile imparted maximum deformation to the target plates followed by flat and ogive nosed projectiles. Numerical investigation of the problem was carried out using finite element code ABAQUS [10]. An axi-symmetric geometric model of the bullet and target plates was made using preprocessing module of the code. Adaptive meshing was used to avoid the excessive distortion of the elements. Analysis of the problem was carried out using explicit solution technique of the code. Results obtained from the finite element simulations were compared with those of the

experiments. Good comparison between the two was found. 2. Experimental investigation Experiments were carried out on layered plates of 1100H12 aluminum alloy. Circular target plates of diameter 255 mm were fixed to a thick mounting plate by means of 16 bolts arranged on a 230 mm diameter pitch circle. Target plates of thicknesses 0.5, 0.71, 1 and 1.5 mm arranged in various layered combinations were impacted by flat, ogive and hemispherical nosed projectiles of 19 mm diameter and 52.5 g mass [Fig. 1 (a)]. To study the effect of projectile nose shape, all the other parameters such as mass, diameter and length of the projectiles was kept constant and hence, the projectiles were made hollow. The projectiles were fabricated of EN-24 steel and oil quenched to Rockwell hardness Rc of 47–52. To obtain a constant mass of the projectiles, the wall thicknesses of the projectiles were slightly varied. The wall thicknesses of the flat, ogive and hemispherical nosed projectiles were 2.44, 3.65 and 2.5 mm, respectively. The projectiles were normally impacted on the target plates above the ballistic limit. The distance from the muzzle to the target was 110 mm. After perforation of the target plates, the projectiles were recovered safely from a wooden catcher placed behind the residual velocity set up. No sign of the deformation of the projectiles was observed in any case. A pneumatic gun was used to launch the projectiles at different velocities [Fig. 1 (b)]. Impact velocity of the projectiles was measured with the help of a photo gate type arrangement comprising of three infrared lightemitting diodes and three infrared light-sensing photodiodes. The residual velocity of the projectiles was measured fairly accurately with the help of two sets of aluminum foil screens of 6 mm thickness pasted firmly on either side of 1.8 mm thick card board having a circular hole of 100 mm at its center. The foils act as a switch and produce signal in the form of voltage rise to the oscilloscope (Gould 1604) as soon as they come in contact. The layered plates were held in contact with each other and fixed firmly on the specimen holding rig along with the two steel rings fastened on either side of the layered plates. 3. Experimental results Experimental results of single as well as layered plates of 0.5, 0.71, 1.0 and 1.5 mm thickness impacted by flat, ogive and hemispherical nosed projectiles are presented in Table 1, 2 and 3, respectively in the form of impact and residual velocities. The target plates were impacted at various velocities at and above the ballistic limit of the projectiles for each layered combination. The velocity drop was found to be higher near the ballistic limit velocity of the projectiles. Typical deformed target specimens impacted by flat, ogive and hemispherical nosed projectiles are shown in Fig. 2 (a), (b) and (c), respectively. It was observed that the flat nosed projectiles failed the target

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

3

a

b COUNTER TIMER-I

DIGITAL STORAGE OSCILLOSCOPE

COUNTER TIMER-II

D.C. AMPLIFIER

ALUMINUM FOILS

PHOTO DIODES RELEASE VALVE

PRESSURE CHAMBER

BARREL PROJECTILE CATCHER

PROJECTILE CHAMBER INFRA-RED REGULATOR

EMMITTERS TARGET PLATE

PRESSURE SOURCE

Fig. 1. (a) Geometry of blunt, hemispherical and ogive nosed projectiles. (b) A schematic of the experimental setup.

plates by removing a circular cap of diameter equal to that of the projectile. The size of the cap was found to be same for each plate in the layered combination. The plastic deformation or dishing, however, varied for each plate. Ogive nosed projectiles caused formation of petals, number of which varied from 6 to 4 with the subsequent layers of the combination. There is a thinning in the region of petal formation, which increases from the root of the petal to its tip. The bending of the petals is found to be almost 901 from the surface of the plate for all the layers except in the case of farthest one in which the petals are bent more than 901. Hemispherical nosed projectiles caused thinning of the target material in the region of contact, and a thin circular plug of considerably smaller diameter than the diameter of the projectile was removed from the target plates. The plug however, remains attached to one of the petals. This phenomenon was observed in all the layered plates of 0.5 mm thickness. For 0.71, 1.0 and 1.5 mm thick-layered plates, however, the plug remained attach to one of the petals of all the layers except the front layer whose plug was completely detached from the target plate. The number of petals formed in the target plates as a result of impact by hemispherical nosed projectiles varied from five to six for different layered combinations. However, the number of petals remained same for all the layers in a layered combination. It was observed however, that the petals in nearer plates are sub-divided in to smaller petals. The

petals are bent up to 901 from the surface of the plate. Highest bending or dishing of the target plates was observed in the case of impact by hemispherical nosed projectiles followed by flat and ogive nosed projectiles. The dishing of the target plates varied for different layers in a layered combination. After the perforation of the projectiles, the consecutive layers of the target plates were found to be in proper contact with each other in the case of impact by ogive and hemispherical nosed projectiles. In the case of flat nosed projectiles, however, surface of the successive layers of the target plates were found to be separated from each other in the region from where the cap was removed, but rest of the layered plates were found in contact with each other. This may be due to the fact that the layered plates impacted by ogive and hemispherical nosed projectiles remained in contact till the end of the perforation phenomenon when the tail of the projectile leaves the last plate of the layered combination. Due to this reason the elastic rebounding of all the layered plates occurred simultaneously. For the case of impact by flat nosed projectiles however, a circular cap was sheared out giving a clean cut to the target plates. As soon as the cap was removed from each plate, the plate lost contact with the projectile, resulting in its elastic rebounding. The number of layers in combination was varied, giving an increased thickness of the target. Figs. 3 (a)–(f) show the impact and residual velocity curves for flat, ogive and

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

0.5

1.0

1.5

2.0

2.5

1

2

3

4

5

0.50

Total thickness (mm)

No. of layers

Target thickness (mm)

1 2 3

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

118.251 113.357 106.97

119.03 111.265 109.523 102.659 97.447 92.572 85.887 73.816 63.264

118.203 112.7 104.37 91.573 90.15 84.7 79.19 67.57 56.382

120.64 116.134 113.92 107.736 98.15 92.336 88.471 81.328 66.93 51.22

113.43 109.79 104.297 101.249 91 88.836 80.446 73.673 65.795 59.887 47.932 35.573

Initial velocity Vi (m/s)

Observed values

89.989 81.311 72.544

91.602 82.231 79.39 69.846 61.876 53.659 41.422 23.593 0

98.771 90.931 80.797 64.433 55.876 46.928 40.115 21.254 0

105.283 99.53 95.51 86.436 75.204 66.929 60.449 49.618 29.63 0

102.81 96.71 89.725 85.778 74.88 71.603 59.281 49.743 38.579 27.125 10.9 0

Residual velocity Vr (m/s)

118.251 113.357 106.97

119.03 111.265 109.523 102.659 97.447 92.572 85.887 73.816 67.2

118.203 112.7 104.37 91.573 90.15 84.7 79.19 67.57 59.6

120.64 116.134 113.92 107.736 98.15 92.336 88.471 81.328 66.93 58.634

113.43 109.79 104.297 101.249 91 88.836 80.446 73.673 65.795 59.887 47.932 43.2

Initial velocity Vi (m/s)

Predicted values

88.78 78.692 68.816

94.389 83.383 80.622 67.914 59.333 51.82 38.756 20.116 0

101.41 93.54 82.599 62.37 59.218 50.965 42.426 26.21 0

109.008 102.993 98.247 89.162 74.96 65.671 58.808 44.605 25.995 0

106.35 100.6 91.834 85.51 72.18 68.512 56.766 47.122 34.422 24.593 8.596 0

Residual velocity Vr (m/s)

4

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 11 12

S. No.

Table 1 Observed and predicted impact (Vi) and Residual (Vr) velocities of blunt nosed projectiles impacted on single and layered plates of various thicknesses

ARTICLE IN PRESS

N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

1.0

0.71

2.13

2.84

3

4

1.0

1.42

2

1

0.71

1

1 2 3 4 5 6 7

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 11

1 2 3 4 5 6 7 8 9

4 5 6 7 8

115.6 104.036 102.5 92.455 87.455 73.986 61.3

120.762 112.989 109.36 104.756 96.22 89.316 84.432 73.729

120.057 113.756 107.873 99.667 93.291 89.692 82.669 76.437 69.18 64.527

117.327 112.376 110.128 103.295 94.24 91.648 86.137 78.613 69.366 63.412 56.531

114.301 101.01 98.27 97.5 82.209 76.214 64.526 51.437 42.793

105.164 102.537 95.68 83.436 70.235

92.985 80.172 79.167 67.454 58.264 43.84 0

82.535 70.843 63.744 55.724 45.086 33.989 24.996 0

91.836 83.141 75.567 63.697 55.668 48.028 39.434 28.824 18.027 0

93.767 86.925 83.302 74.583 62.226 56.182 45.565 32.242 21.039 12.833 0

93.246 78.333 73.382 71.265 56.75 43.802 28.304 12.301 0

69.392 64.016 52.964 30.468 0

115.6 104.036 102.5 92.455 87.455 73.986 66.7

120.762 112.989 109.36 104.756 96.22 89.316 84.432 71.4

120.057 113.756 107.873 99.667 93.291 89.692 82.669 76.437 69.18 66.8

117.327 112.376 110.128 103.295 94.24 91.648 86.137 78.613 69.366 61.7

114.301 101.01 98.27 97.5 82.209 76.214 64.526 51.437 44.3

105.164 102.537 95.68 83.436 78.62

98.661 83.916 82.512 63.302 53.15 40.645 0

83.097 72.058 67.085 59.138 47.894 37.002 27.102 0

96.825 86.541 78.109 65.953 56.966 50.246 38.449 27.224 15.003 0

97.003 89.111 84.196 73.979 58.573 54.236 44.487 31.181 16.593 0

97.432 81.146 76.782 74.987 59.134 48.742 31.236 13.01 0

66.204 59.805 49.173 25.298 0

ARTICLE IN PRESS

N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]] 5

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

1.5

3.0

1

2

3.0

3

1 2 3 4 5 6 7 8 1 2 3 4 5 6

1 2 3 4 5 6 7

1 2 3 4 5 6 7 8 9

S. No.

112.362 107.526 104.821 96.326 85.382 71.432 64.138 56.115 121.476 114.503 109.946 98.073 93.227 86.527

121.144 112.99 107.583 101.66 96.52 91.832 83.471

116.121 111.39 103.122 98.708 95.06 88.624 77.5 71.946 65.774

Initial velocity Vi (m/s)

Observed values

86.88 78.917 74.609 63.39 51.046 33.763 22.672 0 80.698 67.892 57.736 40.181 31.927 0

87.452 72.874 63.819 55.61 40.284 32.159 0

86.378 78.648 66.557 59.328 54.803 45.407 31.384 21.308 0

Residual velocity Vr (m/s)

112.362 107.526 104.821 96.326 85.382 71.432 64.138 58.6 121.476 114.503 109.946 98.073 93.227 84.32

121.144 112.99 107.583 101.66 96.52 91.832 87.6

116.121 111.39 103.122 98.708 95.06 88.624 77.5 71.946 68.8

Initial velocity Vi (m/s)

Predicted values

82.993 74.789 69.696 58.326 45.741 28.181 17.958 0 81.244 69.86 60.02 44.698 35.965 0

86.924 69.202 60.047 49.456 36.297 25.67 0

88.598 77.963 64.373 57.397 49.831 39.353 24.82 16.491 0

Residual velocity Vr (m/s)

6

1.5

2.0

2

1.0

Total thickness (mm)

No. of layers

Target thickness (mm)

Table 1 (continued )

ARTICLE IN PRESS

N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

0.5

1.0

1.5

2.0

2.5

1

2

3

4

5

0.5

Total thickness (mm)

No. of layers

Target thickness (mm)

1 2 3 4

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 11

S. No.

117.662 113.88 105.53 98.436

122.476 115.037 106.775 104.89 98.28 87.688 79.466 67.512 61.692

119.42 113.706 110.568 105.12 97.595 93.163 86.133 72.247 66.753 50.963

116.198 110.447 103.521 95.264 89.55 85.611 77.4 64.461 54.771 39.188

107.805 97.885 92.46 83.892 77.41 69.638 62.472 54.102 47.468 40.665 33.749

Initial velocity Vi (m/s)

Observed values

88.226 82.211 69.589 60.436

97.913 85.343 74.254 71.284 60.438 47.635 36.131 18.73 0

102.648 95.492 91.198 82.01 70.568 62.649 49.989 30.619 18.636 0

104.961 96.914 85.878 73.993 64.497 56.894 43.269 25.351 12.006 0

99.423 88.72 81.783 68.437 58.217 48.114 38.807 27.629 17.153 8.038 0

Residual velocity Vr (m/s)

117.662 113.88 105.53 98.436

122.476 115.037 106.775 104.89 98.28 87.688 79.466 67.512 60.7

119.42 113.706 110.568 105.12 97.595 93.163 86.133 72.247 66.753 59.2

116.198 110.447 103.521 95.264 89.55 85.611 77.4 64.461 54.771 41.3

107.805 97.885 92.46 83.892 77.41 69.638 62.472 54.102 47.468 40.6

Initial velocity Vi (m/s)

Predicted values

Table 2 Observed and predicted impact (Vi) and residual (Vr) velocities of ogive nosed projectiles impacted on single and layered plates of various thicknesses

92.124 84.408 69.863 60.301

105.541 90.289 79.735 75.935 65.453 52.572 38.93 21.112 0

108.966 100.49 94.069 83.762 68.678 60.701 45.761 26.949 14.316 0

109.481 99.89 88.828 75.9 67.013 58.494 46.137 29.725 14.853 0

100.482 87.47 79.49 65.576 54.642 45.336 36.131 23.96 14.042 0

Residual velocity Vr (m/s)

ARTICLE IN PRESS

N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]] 7

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

0.71

1.42

2.13

2.84

1

2

3

4

0.71

Total thickness (mm)

No. of layers

Target thickness (mm)

Table 2 (continued )

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9 10 118.708 111.593 107.737 104.439 97.699 92.219 83.263 76.44 69.275

114.58 108.73 103.681 96.072 94.673 87.23 81.516 75.436 69.174 62.55

111.957 105.13 100.37 94.629 92.664 87.55 79.268 73.475 64.761 57.072 51.158

114.94 111.061 103.007 97.885 88.325 72.258 64.993 51.249 44.255 38.406

94.88 83.725 76.265 65.991

Initial velocity Vi (m/s)

Observed values

91.578 77.841 68.002 62.722 49.314 41.69 28.836 16.761 0

91.108 80.79 72.012 61.53 54.914 45.113 35.191 25.212 14.826 0

95 85.248 79.6 70.768 65.532 56.078 43.534 34.842 21.136 9.737 0

103.72 99.384 90.423 83.384 69.983 48.578 38.859 19.588 8.485 0

54.107 36.514 24.681 0

Residual velocity Vr (m/s)

118.708 111.593 107.737 104.439 97.699 92.219 83.263 76.44 74.7

114.58 108.73 103.681 96.072 94.673 87.23 81.516 75.436 69.174 67.3

111.957 105.13 100.37 94.629 92.664 87.55 79.268 73.475 64.761 57.072 54.6

114.94 111.061 103.007 97.885 88.325 72.258 64.993 51.249 44.255

94.88 83.725 76.265 69.46

Initial velocity Vi (m/s)

Predicted values

94.056 80.365 69.965 62.128 47.919 35.779 24.236 13.06 0

95.044 84.109 73.244 60.561 53.981 41.873 32.286 21.71 10.994 0

98.413 87.768 79.927 71.77 68.046 57.298 45.995 35.84 22.161 8.257 0

101.98 97.227 86.009 76.232 62.686 42.784 31.749 13.98 0

52.967 31.535 20.793 0

Residual velocity Vr (m/s)

8

1 2 3 4 5 6 7 8 9 10 11

1 2 3 4 5 6 7 8 9 10

5 6 7 8

S. No.

ARTICLE IN PRESS

N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

1.5

3.0

1

2

3

3

1.5

2.0

2

1.0

1.0

1

1.0

1 2 3 4 5 6 7

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

117.322 110.14 106.655 97.785 89.214 84.243 78.649

112 108.932 106.247 100.2 96.326 88.746 74.644 62.88 54.297

122.56 115.39 107.647 105.311 98.79 86.563 81.43 74.187

119.92 112.056 109.7 102.438 96.215 89.044 76.452 67.438 62.854

112.725 97.236 82.973 81.913 73.307 65.801 57.283 51.279 45.308

80.758 67.391 60.745 47.585 34.839 27.515 0

97.037 87.916 84 75.714 69.975 58.174 39.522 23.467 0

90.359 77.964 66.026 61.545 51.376 36.399 28.209 0

95.257 82.912 75.074 62.552 53.823 43.417 27.321 13.558 0

99.112 78.267 61.622 58.194 44.384 29.687 17.867 8.726 0

117.322 110.14 106.655 97.785 89.214 84.243 80.48

112 108.932 106.247 100.2 96.326 88.746 74.644 62.88 58.6

122.56 115.39 107.647 105.311 98.79 86.563 81.43 78.4

119.92 112.056 109.7 102.438 96.215 89.044 76.452 67.438 63.8

112.725 97.236 82.973 81.913 73.307 65.801 57.283 52.1

82.579 70.717 63.54 45.959 32.582 22.791 0

97.956 88.829 81.284 73.942 67.211 55.236 37.209 20.653 0

93.137 79.793 67.33 61.275 48.925 31.237 20.858 0

100.406 88.829 81.837 68.712 58.766 47.788 29.348 14.775 0

95.64 73.258 55.713 53.277 38.679 26.04 15.939 0

ARTICLE IN PRESS

N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

9

0.5

1.0

1.5

2.0

2.5

1

2

3

4

5

0.5

Total thickness (mm)

No. of layers

Target thickness (mm)

1 2 3 4

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8 9

122.613 116.277 108.345 105.644

114.55 111.667 106.82 98.236 95.764 91.46 84.768 75.229

121.422 114.753 109.665 100.61 97.623 93.602 85.247 78.542 65.179

119.82 112.385 107.08 106.21 97.792 90.35 83.264 76.564 65.271 53.668

118.624 112.43 100.563 94.175 87.516 82.429 78.531 70.251 65.228 57.428 48.526 42.35

Initial velocity Vi (m/s)

Observed values

87.819 79.217 65.529 57.424

83.319 76.947 68.773 55.01 50.914 44.16 30.635 0

95.031 84.246 75.795 62.77 58.724 53.492 37.889 24.569 0

101.38 89.726 82.31 80.887 68.024 57.855 44.148 29.936 13.831 0

107.454 99.265 85.523 75.303 67.932 61.769 56.278 44.936 36.497 25.324 12.843 0

Residual velocity Vr (m/s)

122.613 116.277 108.345 105.644

114.55 111.667 106.82 98.236 95.764 91.46 84.768 78.4

121.422 114.753 109.665 100.61 97.623 93.602 85.247 78.542 70.2

119.82 112.385 107.08 106.21 97.792 90.35 83.264 76.564 65.271 62.4

118.624 112.43 100.563 94.175 87.516 82.429 78.531 70.251 65.228 57.428 48.526 45.1

Initial velocity Vi (m/s)

Predicted values

83.179 74.098 60.683 53.443

79.036 73.974 65.592 51.529 47.578 38.818 25.431 0

93.457 82.209 72.505 59.397 54.797 48.438 33.555 21.196 0

102.493 89.07 81.054 78.882 64.52 53.585 43.044 26.703 7.901 0

108.389 99.813 84.773 74.271 66.716 58.903 52.368 39.802 31.811 21.956 9.418 0

Residual velocity Vr (m/s)

10

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 11 12

S. No.

Table 3 Observed and predicted impact (Vi) and residual (Vr) velocities of hemispherical nosed projectiles impacted on single and layered plates of various thicknesses

ARTICLE IN PRESS

N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

1.0

0.71

2.13

2.84

3

4

1.0

1.42

2

1

0.71

1

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

5 6 7 8

116.532 112.427 108.131 105.251 98.314 91.91 80.692 72.4 62.174

122.79 116.869 111.137 107.451 105.397 98.647 93.526 85.116 80.204

120.315 114.756 109.223 99.672 93.88 85.469 78.637 76.466 69.344

115.313 107.624 102.634 97.163 93.047 87.77 80.672 72.505 63.314

115.31 112.007 98.541 90.383 79.412 71.626 65.361 54.612 46.883

97.569 92.332 86.217 79.369

95.4 88.757 83.831 78.371 69.784 60.29 45.247 33.844 0

93.149 78.209 69.59 60.737 54.217 40.874 32.106 17.74 0

92.892 78.976 70.21 56.205 47.671 35.331 24.313 19.195 0

87.949 73.83 66.996 57.438 51.503 44.7 33.371 20.727 0

102.67 97.394 81.827 70.875 51.55 42.179 30.789 14.639 0

43.445 35.722 24.512 0

116.532 112.427 108.131 105.251 98.314 91.91 80.692 72.4 67.1

122.79 116.869 111.137 107.451 105.397 98.647 93.526 85.116 82.5

120.315 114.756 109.223 99.672 93.88 85.469 78.637 76.466 73.6

115.313 107.624 102.634 97.163 93.047 87.77 80.672 72.505 68.3

115.31 112.007 98.541 90.383 79.412 71.626 65.361 54.612 51.4

97.569 92.332 86.217 82.5

96.681 86.321 79.885 74.405 64.551 53.261 36.455 24.939 0

89.131 76.634 66.443 57.566 48.98 38.377 27.203 13.952 0

88.743 76.903 65.967 51.997 42.636 30.279 19.413 13.993 0

85.7 70.679 63.068 54.371 47.929 40.544 28.492 15.882 0

98.954 92.793 76.685 66.23 48.164 38.006 28.089 12.19 0

39.177 31.917 19.957 0

ARTICLE IN PRESS

N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]] 11

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

1.5

3.0

1

2

3.0

3

1 2 3 4 5 6 1 2 3 4

1 2 3 4 5

1 2 3 4 5 6 7

S. No.

110.375 106.337 98.256 83.614 75.544 69.492 118.956 115.627 106.113 96.75

120.53 113.25 107.814 98.2 91.658

118.755 111.858 109.164 102.766 94.52 87.684 83.056

Initial velocity Vi (m/s)

Observed values

78.928 65.142 50.943 31.431 18.833 0 69.736 58.745 42.699 0

75.858 60.491 47.351 28.427 0

80.112 70.168 66.862 54.935 41.897 27.519 0

Residual velocity Vr (m/s)

110.375 106.337 98.256 83.614 75.544 71.8 118.956 115.627 106.113 99.12

120.53 113.25 107.814 98.2 93.2

118.755 111.858 109.164 102.766 94.52 87.684 84.3

Initial velocity Vi (m/s)

Predicted values

74.423 63.086 50.243 28.952 16.065 0 61.659 52.191 36.233 0

71.314 57.12 43.112 26.989 0

76.029 66.616 61.805 49.805 37.256 23.256 0

Residual velocity Vr (m/s)

12

1.5

2.0

2

1.0

Total thickness (mm)

No. of layers

Target thickness (mm)

Table 3 (continued )

ARTICLE IN PRESS

N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

13

Fig. 2. Deformed specimens of layered target plates impacted by (a) blunt nosed projectiles; (b) ogive nosed projectiles; (c) hemispherical nosed projectiles.

hemispherical nosed projectiles impact on various layered plates of 0.5 and 1.0 mm thicknesses. It is observed that the velocity drop of the projectiles increases with an increase in the number of layers of the target plate. The velocity drop, however, decreases with an increase in the impact velocity. The highest velocity drop of the projectiles is observed at the ballistic limit velocity. Nose shape of the projectile is an important factor affecting the mechanism of deformation, and hence the resistance offered by the target plates. Impact and residual velocity curves of various nose shapes of the projectiles are plotted to evaluate the energy absorption capacity of the target plates. Figs. 4 (a)–(f) show the comparison of flat, ogive and hemispherical nosed projectiles as a result of impact on various layered combinations of different thicknesses. It is observed that the ogive nosed projectile is the most efficient penetrator of the target plates and consequently has lowest ballistic limit velocity. Flat nosed projectile is found to be comparable to that of the ogive nosed projectile except in the case of two layers of 0.71 and 1.5 mm thicknesses in which the earlier one absorbed more energy as compared to the latter. Hemispherical nosed projectile however, found to be the least efficient pene-

trator of the target plates and showed highest ballistic limit velocity in all the cases. To study the efficiency of single and layered plates impacted by projectiles of various nose shapes, the impact and residual velocities of projectiles for a single plate are compared to that of the layered combination of equivalent thickness. A typical comparison of single and layered plates of various thicknesses is shown in Figs. 5 (a)–(p). It is observed that the residual velocity of the projectiles for a combination of two layers is comparable to that of the single plate of equivalent thickness in all the cases of impact except in the case of ogive nosed projectile impact on two layers of 1 and 1.5 mm thicknesses, in which case single plate of equivalent thickness offered more resistance against perforation. When the layered combinations of more than two layers were compared to that of the single plate of equivalent thickness, the later offered greater resistance against projectile perforation. However, when a four-layered combination of 0.5 mm thickness impacted by flat nosed projectile, was compared to a 2 mm thick plate, the residual velocities in both the cases were found to be comparable. The ballistic limit velocity on the other hand was found to be higher for single target plates in all the

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

Residual velocity (m/s).

a

(Blunt nosed projectile case) 120

b

(Ogive nosed projectile case) 120

0.5 mm x 2 0.5 mm x 3 0.5 mm x 4 0.5 mm x 5

100 80 60 40 20

Residual velocity (m/s).

14

80 60 40 20 0

0

30 40 50 60 70 80 90 100 110120 130

40 50 60 70 80 90 100 110 120 130 Impact velocity (m/s) (Hemispherical nosed projectile case)

Residual velocity (m/s).

100

0.5 mm x 2 0.5 mm x 3 0.5 mm x 4 0.5 mm x 5

80 60 40 20

Impact velocity (m/s)

d

1 mm x 2 1 mm x 3

80 60 40 20 0

0

60

50 60 70 80 90 100 110 120 130 Impact velocity (m/s)

e

(Ogive nosed projetile case)

f

60 40 20 0 60

70

80 90 100 110 120 130 Impact velocity (m/s)

Residual velocity (m/s).

1 mm x 2 1 mm x 3

80

70

80

90 100 110 120 130

Impact velocity (m/s)

100 Residual velocity (m/s).

(Blunt nosed projectile case)

100 Residual velocity (m/s).

c

0.5 mm x 2 0.5 mm x 3 0.5 mm x 4 0.5 mm x 5

100

100

(Hemispherical nosed projectile case) 1 mm x 2 1 mm x 3

80 60 40 20 0 70

80

90 100 110 120 Impact velocity (m/s)

130

Fig. 3. Variation of residual velocity with impact velocity for layered plates impacted by blunt, ogive and hemispherical nosed projectiles.

cases except for the case of 2 mm thick single plate compared with two-layered plate of 1 mm thickness impacted by hemispherical nosed projectiles. In this case the ballistic limit velocity of layered combination (83 m/s) was found to be slightly higher than that of the single plate (81.39 m/s). Moreover, for the same combination impacted by blunt nosed projectile the ballistic limit velocity was found to be almost same (65.7 m/s). Deformation profiles of the layered target plates of various thicknesses, impacted by flat, ogive and hemispherical nosed projectiles are plotted in Figs. 6 (a)–(f), showing the typical deformation profiles of various layers of plates of 0.5 and 0.71 mm thicknesses. It is observed that the plastic deformation of the target plates increases with

the successive layer from the front plate. Maximum plastic deformation is observed in the farthest plate of the layered combination. It is also observed that the hemispherical nosed projectile caused highest deformation of the target plates followed by flat and ogive nosed projectiles. 4. Constitutive material modeling To predict the behavior of the target material during numerical simulation of the problem, an elasto-viscoplastic material model presented by Johnson and Cook [11,12] was incorporated. The Von-Mises stress s¯ of the Johnson-Cook model is the product of three material characteristics namely strain hardening, strain rate hardening and

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

a 120

Blunt nose Ogive nose Hemispherical nose

100 80 60 40 20

60 40 20 0

Residual velocity (m/s).

70

Two layers of 0.71 mm thickness

100

60

80 90 100 110 120 130 Impact velocity (m/s)

80 60 40 Blunt nose Ogive nose Hemispherical nose

20

d

60 40 20 0

Residual velocity (m/s).

60 40 20 0 70

80

90 100 110 120 Impact velocity (m/s)

70

80 90 100 110 120 130 Impact velocity (m/s)

Two layers of 1.5 mm thickness

100

Blunt nose Ogive nose Hemispherical nose

80

60

f

Three layers of 1 mm thickness

90 100 110 120 130

Blunt nose Ogive nose Hemispherical nose

80

50 60 70 80 90 100 110 120 130 Impact velocity (m/s) 100

80

Three layers of 0.71 mm thickness

100

0

e

70

Impact velocity (m/s)

Residual velocity (m/s).

60

Residual velocity (m/s).

Blunt nose Ogive nose Hemispherical nose

80

0

c

Five layers of 0.5 mm thickness

100 Residual velocity (m/s).

Residual velocity (m/s).

b

Four layers of 0.5 mm thickness

15

Blunt nose Ogive nose Hemispherical nose

80 60 40 20 0

130

70

80

90 100 110 120 Impact velocity (m/s)

130

Fig. 4. Impact and residual velocity comparison of blunt, ogive and hemispherical nosed projectiles for layered plates of various thicknesses.

temperature softening, and can be expressed as " !# pl h    pl n i _¯ m 1  T^ , s¯ ¼ A þ B ¯ 1 þ C ln _0

(1)

where A, B, C, n, and m are material parameters, ¯ pl is the pl equivalent plastic strain, _¯ is equivalent plastic strain rate, _0 is a reference strain rate, and T^ is the non-dimensional temperature defined below T^ ¼ ðT  T 0 Þ=T melt  T 0

T 0 pTpT melt ,

(2)

where T is the current temperature, Tmelt is the melting point temperature, and T0 is the room temperature.

The proposed fracture model of Johnson and Cook [12] includes the effect of stress triaxiality, strain rate, and temperature in the expression of equivalent failure strain shown below ¯ pl f

" !# pl h  s i   _¯ m ¼ D1 þ D2 exp D3 1 þ D4 ln 1 þ D5 T^ , _0 s¯ (3)

where D1 to D5 are material constants and sm is the mean stress. Fig. 7 shows the true stress-true strain curve of the tested material (aluminum 1100–H12 alloy). The target material was procured from the market in different

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

16

a

Blunt nosed projectile case

80 60 40 20

Ogive nosed projectile case 100

0.5 mm x 2 1 mm Residual velocity (m/s)

Residual velocity (m/s)

100

b

0

0.5 mm x 2 1 mm

80 60 40 20 0 30 40 50 60 70 80 90 100 110 120 Impact velocity (m/s)

40 50 60 70 80 90 100 110 120 130 Impact velocity (m/s)

c

Hemispherical nosed projectile case

d

Blunt nosed projectile case

Residual velocity (m/s)

100

0.5 mm x 2 1 mm

80 60 40 20

Residual velocity (m/s)

100

0

e

Ogive nosed projectile case

60 40 20 0

50 60 70 80 90 100 110 120 130 Impact velocity (m/s)

0.5 mm x 5 2.5 mm

80

60

f

70

80 90 100 110 120 130 Impact velocity (m/s)

Hemispherical nosed projectile case

Residual velocity (m/s)

100

0.5 mm x 5 2.5 mm

80 60 40 20

Residual velocity (m/s)

100

0 60 70 80 90 100 110 120 130 140 Impact velocity (m/s) Blunt nosed projectile case

Residual velocity (m/s).

100

0.5 mm x 4 2 mm

80 60 40 20

60 40 20 0

70

h

80 90 100 110 120 Impact velocity (m/s)

130

Ogive nosed projectile case 100

Residual velocity (m/s).

g

0.5 mm x 5 2.5 mm

80

0.5 mm x 4 2 mm

80 60 40 20 0

0 60

70

80 90 100 110 120 130 Impact velocity (m/s)

60

70

80 90 100 110 120 130 Impact velocity (m/s)

Fig. 5. Impact and residual velocity comparison of single and layered plates of equivalent thickness.

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

j

Hemispherical nosed projectile case

Blunt nosed projectile case

100 0.5 mm x 4 2 mm

80

100 Residual velocity (m/s).

Residual velocity (m/s).

i

17

60 40 20 0

1 mm x 2 2 mm

80 60 40 20 0

70

k

80

90 100 110 120 Impact velocity (m/s)

130

60

l

Ogive nosed projectile case

70

80 90 100 110 120 130 Impact velocity (m/s)

Hemispherical nosed projectile case 100

1 mm x 2 2 mm

Residual velocity (m/s).

Residual velocity (m/s).

100 80 60 40 20 0

1 mm x 2 2 mm

80 60 40 20 0

60 70 80 90 100 110 120 130 140

80

90

Impact velocity (m/s)

m

n

Blunt nosed projectile case

110

120

130

Ogive nosed projectile case 120

1 mm x 3 3 mm

80

Residual velocity (m/s)

Residual velocity (m/s)

100

60 40 20

1 mm x 3 3 mm

100 80 60 40 20 0

0 80

o

90 100 110 120 Impact velocity (m/s)

130

70

p

Blunt nosed projectile case 100 1.5 mm x 2 3 mm

80 60 40 20

80

90 100 110 120 Impact velocity (m/s)

130

Ogive nosed projectile case

100 Residual velocity (m/s)

Residual velocity (m/s)

100

Impact velocity (m/s)

1.5 mm x 2 3 mm

80 60 40 20 0

0 80

90 100 110 120 Impact velocity (m/s)

130

70

80

90 100 110 120 Impact velocity (m/s)

130

Fig. 5. (Continued)

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

a

0.5 mm Thickness (blunt nosed projectile case)

7

Plate 5 Plate 4 Plate 3 Plate 2 Plate 1

Plate deflection (mm)

6 5 4 3 2

b

0.5 mm Thickness (ogive nosed projectile case)

4 Plate deflection (mm)

18

Plate 5 Plate 4 Plate 3 Plate 2 Plate 1

3

2

1

1 0

0

c

0

20 40 60 80 100 120 Distance from the centre of the plate (mm) 0.5 mm Thickness (hemispherical nosed projectile case)

d

7 6 5 4 3 2

5 4 3 2

0.71 mm Thickness (ogive nosed projectile case) 4

Plate 3 Plate 2 Plate 1

3

0

20 40 60 80 100 120 Distance from the centre of the plate (mm)

2

1

0

20

40

60

80

100

120

Distance from the centre of the plate (mm)

f

0.71 mm Thickness (hemispherical nosed projectile case) 9 Plate 3 Plate 2 Plate 1

8 Plate deflection (mm)

0

e

Plate deflection (mm)

6

1

1 0

Plate 3 Plate 2 Plate 1

7 Plate deflection (mm)

Plate deflection (mm)

8

20 40 60 80 100 120 Distance from the centre of the plate (mm) 0.71 mm Thickness (blunt nosed projectile case)

8

9 Plate 5 Plate 4 Plate 3 Plate 2 Plate 1

0

7 6 5 4 3 2 1 0

0 0

20 40 60 80 100 120 Distance from the centre of the plate (mm)

0

20

40

60

80

100

120

Distance from the centre of the plate (mm)

Fig. 6. Comparison of deformation profiles of layered target plates of various thicknesses.

thicknesses and used in as received condition. It was considered that any mechanical treatment given to the target in order to roll it to the required thickness may affect its material properties. In the present study however, the material properties of various target thicknesses are assumed to be same. Detail of the material model as well as identification procedure of various material parameters is presented in Gupta et al. [13]. The numerical value of all material parameters used for the finite element modeling is presented in Table 4.

5. Numerical investigations Numerical simulation of the problem was carried out using finite element code ABAQUS. The explicit solution scheme of the code in conjunction with the Johnson–Cook elasto-viscoplastic model was efficiently used to analyze the problem of projectile impact on layered plates. An axi-symmetric geometric model of the layered target plates and the projectiles was generated in the preprocessing module (ABAQUS/CAE) of the code. The projectile was

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

using post processing module of the code. The post processor of the software generated an output database file that was processed in the Visualization module of finite element code to obtain the results.

350 300 250 True stress

19

200

5.1. Meshing strategy

150 100 50 0 0

0.1

0.2

0.3

0.4 0.5 0.6 True strain

0.7

0.8

0.9

1

Fig. 7. True stress–true strain curve of the target material.

Table 4 Material parameters used for numerical simulation of the problem Modulus of elasticity, E (N/mm2) Poison’s ratio, n Density, r (kg/m3) Yield stress, A (N/mm2) B (N/mm2) n C Reference strain rate, _0 (1/s) M Tmelt (K) T0 (K) Specific heat, Cp (J/kgK) Inelastic heat fraction, Z D1 D2 D3 D4 D5

65.762  103 0.3 2700 148.361 345.513 0.183 0.001 1.0 0.859 893 293 920 0.9 0.071 1.248 1.142 0.147 0.0

considered as an analytical rigid body with a single reference point used to assign the mass and impact velocity to the projectile. The target plates were considered as the deformable body. Contact was assigned between the bullet and the target plates using kinematic contact algorithm. The bullet was considered as the master surface and the contact surface of the plates as the slave surface. The effect of friction between projectile and target was considered as negligible. Contact was also assigned between the contact surfaces of layered plates. The lower surface of the first plate was considered as the master surface and the upper surface of the second plate was considered as the slave surface. Contact was assigned in this manner to all the consecutive layers using kinematic contact algorithm. Frictional effects were incorporated between the contact surfaces of the layered plates by assigning a coefficient of friction of 0.5 that was obtained from the inclined plane experiments. The target plates were restrained at the boundary and the projectile was given an initial velocity equivalent to that measured during the experimental investigation. The program was submitted for the analysis

The proposed finite element model of the bullet and layered target plates prior to impact is shown in Fig. 8. Meshing strategy of the layered plates was influenced by the nose shape of the projectile. Four-noded axi-symmetric quadrilateral elements with single integration point were used for the case of impact by flat and hemispherical nosed projectiles. For the case of ogive nosed projectile impact however, three-noded axi-symmetric triangular elements with single integration point were employed. Triangular elements were incorporated to reduce the distortion of the elements that was more prominent for the case of impact by ogive nosed projectiles. The mesh density was higher in the influenced region where the projectile comes in contact with the target plates. The mesh density was reduced however, as the distance form the impact area increased. The aspect ratio of the elements was maintained as unity in the zone of impact. At the periphery of the plate, however, it was allowed to increase up-to 9 and 1.5 in the case of quadrilateral and triangular elements, respectively. The number of elements in the target plate was varied according to the thickness of the plate. For the case of 0.5, 0.71, 1 and 1.5 mm thick target plates the number of elements in the thickness direction was 9, 13, 18 and 27, respectively. Total number of elements in the target plates was 4554, 6578, 9108 and 13,662, respectively for the case of impact by flat and hemispherical nosed projectiles. For the case impact by ogive nosed projectiles however, the total number of elements in the target plates was 5658, 8367, 11,410 and 17,174 for 0.5, 0.71, 1 and 1.5 mm thick target plates, respectively. 5.2. Adaptive meshing Projectile impact causes severe deformation of the target plates. As a result of which the elements in front of the nose of the projectile get heavily distorted, leading to the penetration of the upper nodes of the critical elements in to the lower nodes, resulting in negative element volume and consequent error termination of the program. To overcome the problem of excessive element distortion adaptive meshing was applied in all the cases of layered target plates impacted by flat, ogive and hemispherical nosed projectiles by creating Lagrangian adaptive mesh domain in the region of the layered target plates directly in front of the projectile and equal to its radius. Adaptive meshing is of great interest in the problem of large deformations, it provides faster, more accurate and robust solution than pure Lagrangian analysis. The frequency of adaptive meshing affects the mesh quality. A new mesh is created for the adaptive mesh domain after a fixed number

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

20

a

Blunt nosed projectile case

b

Ogive nosed projectile case

c

Hemispherical nosed projectile case Fig. 8. Finite element model.

of increments. A typical problem of very high rate of deformation requires a more frequent adaptive meshing. In the present problem adaptive meshing was performed at every five increments of the analysis. In an adaptive mesh increment, a new, smoother mesh is created by sweeping iteratively over the adaptive mesh domain. During each sweep the nodes in the domain are relocated based on the current position of neighboring nodes and elements. In a

typical mesh sweep a node is moved a fraction of the characteristic length of any element surrounding that node. Increasing the number of mesh sweeps increases the intensity of adaptive meshing. In the present case, 100 mesh sweeps were performed during each adaptive remeshing. In a few cases of ogive nosed projectile impact, however, adaptive meshing of higher intensity was performed to run the program till completion.

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

6. Computational results and discussion Numerical results of layered target plates impacted by flat, ogive and hemispherical nosed projectiles are shown in Tables 1–3 respectively. Layered plates of 0.5, 0.71, 1 and 1.5 mm thicknesses arranged in various configurations were impacted by flat, ogive and hemispherical nosed projectiles at varying velocity. It is observed that as the impact velocity of the projectiles increases the velocity drop decreases. The velocity drop however, increases with an increase in the number of layers of the target plate. The highest velocity drop of the projectile is predicted at the ballistic limit velocity. The predicted progress of deformation of the layered target plates as a result of impact by flat, ogive and hemispherical nosed projectiles is shown in Fig. 9. A close agreement is found between the experimental and numerical mechanism of deformation of the layered target plates. For the case of impact by flat nosed projectiles a circular cap of diameter equal to that of the projectile is removed from the target plates. It is also observed that as soon as the plug is removed there is a loss of contact between the target plates that has caused

21

separation of various layers near the impact region. The apparent separation might have occurred due to the elastic rebounding of the plate, since the plate lost contact as soon as the cap is removed. This phenomenon is also observed from the experimental results of flat nosed projectile impact. Ogive nosed projectiles failed the target plates by formation of petals. However, since the present analysis is axi-symmetric, the number of petals could not be predicted. Hemispherical nosed projectiles caused thinning of the target plates and removed thin plugs of considerably smaller diameter than the diameter of the projectile. Highest plastic deformation of the target plates is caused by the impact of hemispherical nosed projectiles followed by flat and ogive nosed projectiles.

6.1. Comparison of observed and predicted results Experimental as well as numerical impact and residual velocities of flat, ogive and hemispherical nosed projectiles are compared as a result of impact on layered target plates

(i) Time:50 µs

(i) Time: 100 µs

(i) Time: 100 µs

(ii) Time: 100 µs

(ii) Time:200µs

(ii) Time: 150 µs

(iii) Time: 150 µs

(iii) Time: 300 µs

(iii) Time: 250 µs

Fig. 9. Predicted progress of deformation of the layered target plates impacted by blunt, ogive and hemispherical nosed projectiles. Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

22

a

b

Five layers of 0.5 mm thickness (blunt nosed projectile case)

100

Experimental Numerical

Residual velocity (m/s).

Residual velocity (m/s).

100 80 60 40 20

60

c

80 90 100 110 Impact velocity (m/s)

60 40 20

120

Experimental Numerical

80

60

d Residual velocity (m/s).

Residual velocity (m/s).

70

Five layers of 0.5 mm thickness (hemispherical nosed projectile case)

100

60 40 20

80

90 100 110 120 Impact velocity (m/s)

130

Two layers of 1.5 mm thickness (ogive nosed projectile case)

100

f

80 60 40 Experimental Numerical

20 0 70

80

90 100 110 120 Impact velocity (m/s)

130

80 90 100 110 Impact velocity (m/s)

120

80 60 40 20

80

Residual velocity (m/s).

70

70

Two layers of 1.5 mm thickness (blunt nosed projectile case)

0 80

0

Residual velocity (m/s).

Experimental Numerical

80

0

0

e

Five layers of 0.5 mm thickness (ogive nosed projectile case)

60

Experimental Numerical

90 100 110 120 Impact velocity (m/s)

130

Two layers of 1.5 mm thickness (hemispherical nosed projectile case) Experimental Numerical

40

20

0 90

100 110 120 Impact velocity (m/s)

130

Fig. 10. Comparison of observed and predicted residual velocities.

of various thicknesses. Figs. 10 (a)–(f) compare a few typical cases of observed and predicted impact and residual velocity. A maximum deviation of 10.66%, 5.0% and 3.79% is found between the observed and predicted ballistic limit velocity of flat, ogive and hemispherical nosed projectiles, respectively, as a result of impact on fivelayered plates of 0.5 mm thickness. Similarly for the case of impact on two layers of 1.5 mm thickness a difference of 2.55%, 2.27% and 2.39% is found between the observed and predicted ballistic limit velocity of flat, ogive and hemispherical nosed projectiles, respectively.

6.2. Contour plots of the layered target plates Contours are plotted in Fig. 11 to explain the variation of stress and strain in the layered target plates as a result of impact by flat, ogive and hemispherical nosed projectiles. In case of flat nosed projectile impact both the VonMises as well as shear stress increase and reach to a maximum value in the front target plate at the region of contact with the edge of the projectile. Stresses further increase and reach to their peak value in the front plate at the time of fracture. Subsequent the fracture of the front

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

S, Mises (Ave. Crit .: 75%) +5.115e+08 +4.688e+08 +4.262e+08 +3.836e+08 +3.410e+08 +2984e+08 +2.557e+08 +2.131e+08 +1.705e+08 +1.279e+08 +8.524e+08 +4.262e+08 +0.000e+00

S, S12 (Ave. Crit .: 75%) +2.451e+08 +2.025e+08 +1.598e+08 +1.171e+08 +7.449e+08 +3.182e+08 -1.084e+08 -5.351e+08 -9.617e+08 -1.388e+08 -2.242e+08 -2.668e+08

PEEQ (Ave. Crit .: 75%) +2.817e+00 +2.582e+00 +2.347e+00 +2.112e+00 +1.878e+00 +1.648e+00 +1.408e+00 +1.174e+00 +9.389e-01 +7.041e-01 +4.694e-01 +2.347e-01 +0.000e+00

S, Mises (Ave. Crit.: 75%) +5.425e+08 +4.973e+08 +4.521e+08 +4.069e+08 +3.616e+08 +3.164e+08 +2.712e+08 +2.260e+08 +1.808e+08 +1.356e+08 +9.041e+07 +4.521e+07 +0.000e+00

S, S12 (Ave. Crit .: 75%) +1.529e+08 +1.306e+08 +1.083e+08 +8.607e+07 +6.380e+07 +4.153e+07 +1.926e+07 -3.010e+06 -2.528e+07 -4.755e+07 -6.982e+07 -9.209e+07 -1.144e+08

PEEQ (Ave. Crit .: 75%) +2.155e+00 +1.975e+00 +1.796e+00 +1.616e+00 +1.437e+00 +1.257e+00 +1.078e+00 +8.979e+00 +7.183e-01 +5.388e-01 +3.592e-01 +1.796e-01 +0.000e+00

23

S, Mises (Ave. Crit .: 75%) +5.040e+08 +4.620e+08 +4.200e+08 +3.780e+08 +3.360e+08 +2.940e+08 +2.100e+08 +2.520e+08 +1.680e+08 +1.260e+08 +8.401e+07 +4.200e+07 +0.000e+00

S, S12 (Ave. Crit .: 75%) +2.018e+08 +1.744e+08 +1.469e+08 +1.194e+08 +9.187e+07 +6.438e+07 +3.688e+07 +9.390e+06 -1.810e+07 -4.560e+07 -7.309e+07 -1.006e+08 -1.281e+08

PEEQ (Ave. Crit .: 75%) +1.134e+00 +1.039e+00 +9.447e-01 +8.502e-01 +7.558e-01 +6.613e-01 +5.668e-01 +4.723e-01 +3.779e-01 +2.834e-01 +1.889e-01 +9.447e-02 +0.000e+00

Fig. 11. Predicted contours of Von-Mises stress, shear stress and equivalent plastic strain for blunt, ogive and hemispherical nosed projectiles.

target plate the stresses reach to a maximum value in the rear plate following the same pattern. The equivalent plastic strain in the layered target plate reaches to a peak value in the front plate on commencement of fracture. The concentration of the plastic strain is highest at the region of detachment of plug.

For the case of impact by ogive nosed projectile the maximum Von-Mises stress develops at the region of layered target plate in contact with the projectile. The concentration of shear stress, however, is highest at the severely bent region of target plates slightly away from the contact region. The bending of the target plates due to

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004

ARTICLE IN PRESS 24

N.K. Gupta et al. / International Journal of Impact Engineering ] (]]]]) ]]]–]]]

onward movement of the projectile causes increase in both the stresses. The stresses become almost constant as soon as the ogival portion of the projectile perforates the layered target plate. The equivalent plastic strain reaches to its peak value at the commencement of perforation when the nose of the projectile burst the layered target plate. The intensity of the plastic strain decreases afterwards and becomes almost constant subsequent the perforation of ogival portion of the projectile. Hemispherical nosed projectile bends the layered target plate as soon as it comes in contact. Bending is higher at the region of contact where the target plates confirm the nose shape of the projectile. The same region experiences the maximum Von-Mises as well as shear stress. As soon as the fracture of the target plates accomplished, the VonMises stress rapidly increases at the region of disengagement of plugs and reaches to its peak value when the hemispherical portion of the projectile completes its passage. The shear stress reaches to its peak value at the commencement of fracture. The equivalent plastic strain increases following the perforation of the target plates. After the separation of the plugs from the layered target plate the equivalent plastic strain further increases and later becomes almost constant when the hemispherical portion of the projectile completes its passage. 7. Conclusions Layered aluminum plates of various thicknesses, arranged in different combinations were impacted at and above the ballistic limit velocity by flat, ogive and hemispherical nosed steel projectiles of 19 mm diameter. It was observed that flat nosed projectiles failed the target plates by removing a circular plug of diameter equal to that of the projectile. Ogive nosed projectiles failed the target plates by forming petals. Highest number of petals was formed in the front target plate. The number of petals decreased with the consecutive layer towards the rare most plate. The petals were bent approximately at 901 from the surface of the plates except the farthest one in which the bending of the petals was more than 901. Hemispherical nosed projectiles caused thinning of the target material and removed thin circular plug of considerably smaller diameter than the diameter of the projectile. Ogive nosed projectiles were found to be the most efficient penetrator as they required lowest energy to perforate. Energy absorbed by the target plates in the case of impact by flat nosed projectiles was found comparable to that of the ogive nosed projectiles except in the case of two and four-layered plate of 0.71 mm and two-layered plate of 1.5 mm thicknesses in which the former one required more energy to perforate. Hemispherical nosed projectiles were found to be the least efficient penetrator of the target plates and hence acquired highest ballistic limit

velocity in all the cases. The ogive nosed projectiles on the other hand were found to have lowest ballistic limit velocity in all the cases. The ballistic limit of blunt nosed projectiles was in-between the hemispherical and ogive nosed projectiles. It was observed that for two layers, the residual velocities of the projectiles were comparable to that of the single plates of equivalent thicknesses. When the number of layers was increased, however, the single plate of equivalent thickness offered more resistance against perforation. The plastic deformation of the target plates increases with each successive layer. Hemispherical nosed projectiles imparted highest plastic deformation to the target plates followed by flat and ogive nosed projectiles, respectively. Numerical simulation of the problem was carried out using finite element code ABAQUS. The predicted and actual impact and residual velocity curves for flat, ogive and hemispherical nosed projectiles showed good agreement. References [1] Marom I, Bonder SR. Projectile perforation of multi-layered beams. Int J Mech Sci 1979;21:489–504. [2] Corran RSJ, Shadbolt PJ, Ruiz C. Impact loading of plates––an experimental investigation. Int J Impact Eng 1983;1(1):3–22. [3] Radin J, Goldsmith W. Normal projectile penetration and perforation of layered targets. Int J Impact Eng 1988;7:229–59. [4] Nurick GN, Walters CE. The ballistic penetration of multiple thin plates separated by an air gap. In: Proceedings of SEM conference on experimental mechanics, The Society of Experimental Mechanics, Inc., 1990. p. 631–7. [5] Gupta NK, Madhu V. Normal and oblique impact of a kinetic energy projectile on mild steel plates. Int J Impact Eng 1992;12:333–43. [6] Gupta NK, Madhu V. An experimental study of normal and oblique impact of hard-core projectile on single and layered plates. Int J Impact Eng 1997;19:395–414. [7] Johnson GR, Cook WH. Lagrangian EPIC code computations for oblique, yawed-rod impacts onto thin-plate and spaced-plate targets at various velocities. Int J Impact Eng 1993;14:373–83. [8] Borvik T, Langseth M, Hopperstad OS, Malo KA. Perforation of 12 mm thick steel plates by 20 mm diameter projectiles with flat, hemispherical and conical noses part I: experimental study. Int J Impact Eng 2002;27:19–35. [9] Borvik T, Langseth M, Hopperstad OS, Malo KA. Perforation of 12 mm thick steel plates by 20 mm diameter projectiles with flat, hemispherical and conical noses part II: numerical simulations. Int J Impact Eng 2002;27:37–64. [10] ABAQUS/Explicit user’s manual. Version 6.3: vol. 1(2), 2002. [11] Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the seventh international symposium on ballistics, The Hague, 1983. [12] Johnson GR, Cook WH. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 1985;21(1):31–48. [13] Gupta NK, Iqbal MA, Sekhon GS. Experimental and numerical studies on the behavior of thin aluminum plates subjected to impact by flat- and hemispherical-nosed projectiles. Int J Impact Eng 2006; 32: 1921–44.

Please cite this article as: Gupta NK, et al. Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2006.11.004